We demonstrate mode-locking of a thulium-doped fiber laser operating at 1.94 μm, using a graphene-polymer based saturable absorber. The laser outputs 3.6 ps pulses, with ~0.4 nJ energy and an amplitude fluctuation ~0.5%, at 6.46 MHz. This is a simple, low-cost, stable and convenient laser oscillator for applications where eye-safe and low-photon-energy light sources are required, such as sensing and biomedical diagnostics.